We follow the outline
of the proof of Theorem 4.2.1 in [1]}.
We take the scalar function \(\zeta \)  corresponding to \(B^1_r(a)\)  and \(\alpha \)  from
Lemma REF  and take a nonnegative function \(\phi =\phi (x^{\prime })\in C^{\infty }_0(B^{\prime }_1(0))\)  with unit integral. Denote \(\eta (x^{\prime })=r^{-d+1}\phi (\frac{x^{\prime }}{r})\) , \(D_r(a):=(a-r,a+r)\times B^{\prime }_r(0)\)  as before, and for \(t\in (0,r^2)\)  set
\(\bar{u}(t):=\int _{D_r(a)}\zeta (y^1)\eta (y^{\prime })u(t,y)\nu _{\alpha }(dy).\nonumber \) 
